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<p>This paper focuses on the analysis of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(L_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(L_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> performance for a class of linear systems which includes the time-varying uncertain parameters and additive delay components. A basic state-feedback controller is designed to overcome the arduous induced by the norm-bounded uncertainties involved in the plant. With the framework of linear matrix inequality (LMI) and the theory of Lyapunov stability analysis, several sufficient conditions are proposed that ensure <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(L_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-<InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(L_{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> performance and stabilization criterion of uncertain linear additive time-delay systems are proposed. This report goes beyond the existing literature by extending basic results on robust performance analysis to time-delay systems with additive delay factors, using the relaxed-based integral inequality (RII). The correctness and advantages of these theoretical records are verified by some numerical examples along with their diagrammatic visualization.</p>

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Improved Results on \(L_2\)-\(L_\infty \) Performance Analysis for Additive Time-Delay Systems having Norm-Bounded Uncertain Components

  • 期刊论文

  • 发表日期：

    2025年10月25日

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  • G. Soundararajan,
  • C. Karthik,
  • Ardak Kashkynbayev,
  • G. Nagamani

摘要

This paper focuses on the analysis of \(L_{2}\) L 2 - \(L_{\infty }\) L ∞ performance for a class of linear systems which includes the time-varying uncertain parameters and additive delay components. A basic state-feedback controller is designed to overcome the arduous induced by the norm-bounded uncertainties involved in the plant. With the framework of linear matrix inequality (LMI) and the theory of Lyapunov stability analysis, several sufficient conditions are proposed that ensure \(L_{2}\) L 2 - \(L_{\infty }\) L ∞ performance and stabilization criterion of uncertain linear additive time-delay systems are proposed. This report goes beyond the existing literature by extending basic results on robust performance analysis to time-delay systems with additive delay factors, using the relaxed-based integral inequality (RII). The correctness and advantages of these theoretical records are verified by some numerical examples along with their diagrammatic visualization.